具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子

王旦霞; 王银珠

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具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子

更新时间：2026-09-14

- 具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子
- 具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子
- Issue 1, (2012)
- 作者机构：
  
  1. 太原理工大学数学学院
  2. 太原科技大学应用科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2012
- 稿件说明：
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王旦霞, 王银珠. 具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子[J]. 2012, (1).
DOI：

王旦霞, 王银珠. 具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子[J]. 2012, (1). DOI：

摘要

对具有结构阻尼和外阻尼的更一般的非线性粘弹性梁方程

在夹钳边界条件和初始条件下

利用Galerkin方法

并结合先验估计

证明了系统的整体强解的存在唯一性;通过先验估计

并结合一些不等式

证明了系统的有界吸收集的存在性;利用已知的验证紧性的方法

证明了系统所确定的半群的紧致性

从而证明了非线性粘弹性梁方程系统的强的整体吸引子的存在性.

Abstract

A generalized nonlinear equation of elastic beam with both structural damping and external damping was considered.By using Galerkin method combined with prior estimates

the existence and uniqueness of global strong solutions were proved under hinged boundary conditions and initial conditions.Through the prior estimates and some inequality

the existence of the bounded absorbing set of above-mentioned system was obtained.By taking the proposed method for compact property verification

the compactness of group determined by the above system was proved

and the existence of the strong global attractor of beam equation was proved.

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